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Charge-charge, current-current, and Raman correlation functions are derived in a consistent way using the unified response theory. The theory is based on the improved description of the conduction electron coupling to the external electromagnetic fields, distinguishing further the direct and indirect ͑assisted͒ scattering on the quasistatic disorder. The two scattering channels are distinguished in terms of the energy and momentum conservation laws. The theory is illustrated on the Emery three-band model for the normal state of the underdoped high-T c cuprates which includes the incoherent electron scattering on the disorder associated with the quasistatic fluctuations around the static antiferromagnetic ͑AF͒ ordering. It is shown, for the first time consistently, that the incoherent indirect processes dominate the low-frequency part of the Raman spectra, while the long-range screening which is dynamic removes the long-range forces in the A 1g channel. In the mid-infrared frequency range the coherent AF processes are dominant. In contrast to the nonresonant B 1g response, which is large by itself, the resonant interband transitions enhance both the A 1g and B 1g Raman spectra to comparable values, in good agreement with experimental observation. It is further argued that the AF correlations give rise to the mid-infrared peak in the B 1g Raman spectrum, accompanied by a similar peak in the optical conductivity. The doping behavior of these peaks is shown to be correlated with the linear doping dependence of the Hall number, as observed in all underdoped high-T c compounds.

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A systematic method of calculating the dynamical conductivity tensor in a general multiband electronic model with strong boson-mediated electron-electron interactions is described. The theory is based on the exact semiclassical expression for the coupling between valence electrons and electromagnetic fields and on the self-consistent Bethe-Salpeter equations for the electron-hole propagators. The general diagrammatic perturbation expressions for the intraband and interband singleparticle conductivity are determined. The relations between the intraband Bethe-Salpeter equation, the quantum transport equation and the ordinary transport equation are briefly discussed within the memory-function approximation. The effects of the Lorentz dipole-dipole interactions on the dynamical conductivity of low-dimensional spα models are described in the same approximation. Such formalism proves useful in studies of different (pseudo)gapped states of quasi-one-dimensional systems with the metal-to-insulator phase transitions and can be easily extended to underdoped two-dimensional high-Tc superconductors.

Recent works 1 "" 5 have shown that the unusual physical properties of high superconducting A 3 B type of intermetallic compounds, such as V 3 Si and Nb 3 Sn, could be understood on the basis of a very fine d-band structure. The Fermi level Ey in the normal state should fall in a very narrow peak of the density of states n(E). This peak lies just above the bottom E m of a nearly empty d sub-band (Fig. 1). Detailed calculations show that the energy range EY~E m of occupied states in the peak is much smaller than the width HOOJJ of the phonon spectrum and of the order of the superconductive gap. For instance, in V 3 Si, EY~E m in the normal state should be equal to 18 xlO"" 4 eV ^22°K. The same situation seems to arise in Nb 3 Sn.In the usual BCS theory the energy-range limitation to the attractive interaction between two pairing electrons arises from the narrowness of the phonon spectrum. On the contrary, assuming here that the d electrons are the superconducting ones, 6 we may expect the energy-range limitation to be imposed by the narrowness of the electronic spectrum. So the exact value of Hoop would not influence the energy gap, in agreement with the extreme smallness of the observed isotopic effect in Nb 3 Sn. 7 Moreover, the very large density of states near the bottom of the d sub-band is related to a Bloch energy E(k) which varies slowly with the wave vector k. The variation with k of the kinetic energy £=£(&)-£jp of the Bloch states involved is small compared with the energy gap A. This fact brings such compounds near to the strong-coupling limit of superconductivity where all the electrons can be involved in Cooper pairs, owing to their nearly equal kinetic energy. If Q is the small number of d electrons present in the peak of Fig. 1, and if we neglect contributions from other bands, two equations must be solved in the BCS formalism 8 to obtain the gap A at absolute zero:V is the BCS coupling constant; w(f) is the density of states for one spin direction. It is given by 1 n(£)=B(£-£ )-1/2 , mwhere B is a normalization constant.For small Q, all the electrons involved are in the peak of n(f). Thus the upper limit in Eqs. (1) and (2), being large compared with the width of this peak, is not important (Fig. 1). We shall take it as infinite.By introducing the new variable x = A~1 /2 (£ ~£ m ) 1/2 , Eqs. (1) and (2) lead to Q = 2B 2 VIJ, A = B 2 V 2 J 2 with •n